Quality and Cost of Deterministic Network Calculus - Design and Evaluation of an Accurate and Fast Analysis

TL;DR

This paper introduces a new algebraic DNC algorithm that significantly improves accuracy and reduces computational costs, challenging the scalability of existing optimization-based methods for network delay analysis.

Contribution

A novel algebraic DNC algorithm that matches the accuracy of optimization-based methods while drastically reducing computational costs.

Findings

Delay bounds deviate by only 1.142% on average from optimization-based bounds.

Analysis times decrease by several orders of magnitude.

Algebraic DNC can be improved to rival optimization-based accuracy.

Abstract

Networks are integral parts of modern safety-critical systems and certification demands the provision of guarantees for data transmissions. Deterministic Network Calculus (DNC) can compute a worst-case bound on a data flow's end-to-end delay. Accuracy of DNC results has been improved steadily, resulting in two DNC branches: the classical algebraic analysis and the more recent optimization-based analysis. The optimization-based branch provides a theoretical solution for tight bounds. Its computational cost grows, however, (possibly super-)exponentially with the network size. Consequently, a heuristic optimization formulation trading accuracy against computational costs was proposed. In this paper, we challenge optimization-based DNC with a new algebraic DNC algorithm. We show that: (i) no current optimization formulation scales well with the network size and (ii) algebraic DNC can be considerably improved in both aspects, accuracy and computational cost. To that end, we contribute a novel DNC algorithm that transfers the optimization's search for best attainable delay bounds to algebraic DNC. It achieves a high degree of accuracy and our novel efficiency improvements reduce the cost of the analysis dramatically. In extensive numerical experiments, we observe that our delay bounds deviate from the optimization-based ones by only 1.142% on average while computation times simultaneously decrease by several orders of magnitude.